
Topology is often described as 'rubber sheet' geometry. This is because topology is about the general overall properties of shapes that remain
unchanged as the shape is stretched and distorted. The shape can be stretched in any way imaginable, but as long as it is not torn, then it is regarded as topologically the same object. To a topologist a sphere is
exactly equivalent to an ellipsoid, as is a cube, dodecahedron or other convex polyhedron. (Convex polyhedra are polyhedra whose faces do not penetrate the interior of the polyhedron.)
Metrical properties, such as the distance between two points on a surface, clearly do not interest topologists, as these properties can change
dramatically when the surface is stretched. What topologists want to find are mathematical properties that do not change when the shape is stretched.
The most famous of these topological invariants, as they are called, was discovered by the great 18th Century Swiss mathematician Leonhard Euler
(pronounced Oiler). He found a number, now known as the Euler number, that remains the same for all convex polyhedra. This number is simply F  E + V, where F is the number of face, E is the number of edges and V is
the number of vertices of the polyhedron.
For instance, a cube has 6 faces, 12 edges and 8 vertices, so its Euler number is 2. Likewise, a dodecahedron has 12 faces, 30 edges and 20 vertices, so
its Euler number is also 2. In fact, all convex polyhedra have an Euler number of 2.
